Deformation induced magnetic confinement and isolated flat-bands in graphene

Strain-induced deformations can alter the charge distribution in graphene and hence provide a new way to design its band structure and transport properties. Working with quasi-periodic linear and close-packed Gaussian deformations, we showed that a pseudo-magnetic produces charge confinement at desired locations in graphene. We also found that spatial maps of the density of states exhibit periodic structures known as moir\'{e} patterns [1]. Motivated by these results, we study graphene with different superlattice structures induced by periodic cosine-like deformations and square, triangular and rectangular symmetries. Our analysis shows that it is possible to create isolated flat bands when the superlattice breaks graphene's parity symmetry (sublattice symmetry). The geometry of the substrate controls the flatness of the isolated bands. Our findings can be used to guide potential experimental realizations to produce flat-band systems by design. \underline {[1] Phys. Rev. B 102, 235410(2020)}